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Three identical cubes, each with edge 8 cm, are placed adjacent to each other to form a cuboid. What is the percentage decrease in the total surface a
Question

Three identical cubes, each with edge 8 cm, are placed adjacent to each other to form a cuboid. What is the percentage decrease in the total surface area compared to the sum of surface areas of the three separate cubes? (Rounded off to two decimal places.)

A.

20.24%

B.

25.67%

C.

27.53%

D.

22.22%

Correct option is D

Given:
Edge of each cube = 8 cm
Three identical cubes are joined to form a cuboid.

Formula Used:
Total Surface Area of a cube = 6a26a^2​​
Total Surface Area of a cuboid = 2(lb + bh + hl)

Solution:
Surface area of 1 cube = 6 × 82 8^2​ = 6 × 64 = 384 sq. cm.
Sum of surface areas of 3 separate cubes = 3 × 384 = 1152 sq. cm.
When joined end to end, the dimensions of the cuboid formed are:
Length (l) = 8 + 8 + 8 = 24 cm
Breadth (b) = 8 cm
Height (h) = 8 cm
Surface area of the cuboid = 2(24 × 8 + 8 × 8 + 8 × 24)
Surface area = 2(192 + 64 + 192)
Surface area = 2(448) = 896 sq. cm.
Decrease in surface area = 1152 - 896 = 256 sq. cm.
Percentage decrease = 2561152\frac{256}{1152}​ × 100
Percentage decrease = 29\frac{2}{9}​ × 100 = 22.222...%
Rounded off to two decimal places = 22.22%

Final Answer
So the correct answer is (d)

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